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The mere quoting of the Bible as authoritative doesn’t imply the quoter thinks only the Bible is authoritative. Catholics, after all, cite Scripture in support of their views, yet this doesn’t mean they believe the Bible to be the sole rule of faith.
The Jews of Jesus’ day quoted the Bible to defend their beliefs, but they also followed their traditions (Mt 15:2). Some were legitimate, some not. Look at Jesus’ attack on one of the illegitimate traditions: the Pharisees’ custom of the Corban (Mt 15:4-9).
His attack is taken by some as a rejection of all tradition and as an affirmation of sola scriptura, but it really shows only that he opposed human traditions which contradicted Scripture, not that he rejected all tradition. You can’t conclude, then, from Jesus’ mere citing of the Bible, that one needs to believe only in the Bible or that the Bible is the sole rule of faith and all tradition must be rejected.
Jesus quoted the Old Testament because it’s the word of God and as such is authoritative for settling the theological questions it addresses. Furthermore, because Scripture was accepted by both Jesus and his opponents, he could appeal to it as common ground between them. Here he followed his usual practice of using what his enemies, in theory at least, would accept as binding.
Consider his dispute with the Sadducees in Matthew 22:23-33 over the resurrection of the body. The Sadducees, who accepted as inspired only the Pentateuch (the first five books of the Old Testament), didn’t believe in the resurrection of the body.
In refuting them, Christ quoted only from the Pentateuch (Ex 3:6), not because he didn’t acknowledge other Old Testament books which explicitly mention the resurrection of the body (such as Daniel 12:2, 13), but because the Sadducees didn’t accept these other books. An appeal to an authority which they didn’t accept would have been useless, so Jesus proved his point by referring to one the Sadducees would affirm.